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Handling inconsistency of function equality #1039

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bvssvni opened this issue Apr 26, 2021 · 0 comments
Open

Handling inconsistency of function equality #1039

bvssvni opened this issue Apr 26, 2021 · 0 comments

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@bvssvni
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bvssvni commented Apr 26, 2021

In Poi, since constants are defined as "function of something that returns the constant", e.g. \true, it is possible to prove:

true = id
(= true)(id)
idb(id)
id(id)
id

while the following is also provable due to the function inequalities:

true = id
id = true
false

This means that function equality is inconsistent.

For now, reductions rules are added to override into the second case, while (= true) <=> idb is an equivalence.
This means that the inconsistency disappears when reductions are applied before equivalences.

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